Many projectively unique polytopes

We construct an infinite family of 4-polytopes whose realization spaces have dimension smaller or equal to 96. This in particular settles a problem going back to Legendre and Steinitz: whether and how the dimension of the realization space of a polytope is determined/bounded by its f-vector. From this, we derive an infinite family of combinatorially distinct 69-dimensional polytopes whose realization is unique up to projective transformation. This answers a problem posed by Perles and Shephard in the sixties. Moreover, our methods naturally lead to several interesting classes of projectively unique polytopes, among them projectively unique polytopes inscribed to the sphere. The proofs rely on a novel construction technique for polytopes based on solving Cauchy problems for discrete conjugate nets in S^d, a new Alexandrov--van Heijenoort Theorem for manifolds with boundary and a generalization of Lawrence's extension technique for point configurations.Comment: 44 pages, 18 figures; to appear in Invent. mat

How wide are European borders? New evidence on the integration effects of monetary unions

We use consumer price data for 81 European cities (in Germany, Austria, Switzerland, Italy, Spain and Portugal) to study deviations from the law-of-one-price before and during the European Economic and Monetary Union (EMU) by analysing both aggregate and disaggregate CPI data for 7 categories of goods we find that the distance between cities explains a significant amount of the variation in the prices of similar goods in different locations. We also find that the variation of the relative price is much higher for two cities located in different countries than for two equidistant cities in the same country. Under EMU, the elimination of nominal exchange rate volatility has largely reduced these border effects, but distance and border still matter for intra-European relative price volatility. JEL classification: F40, F4

Economic integration and the exchange rate regime: how damaging are currency crises?

We use consumer price data for 205 cities/regions in 21 countries to study deviations from the law-of-one-price before, during and after the major currency crises of the 1990s. We combine data from industrialised nations in North America (Unites States, Canada, Mexico), Europe (Germany, Italy, Spain and Portugal) and Asia (Japan, Korea, New Zealand, Australia) with corresponding data from emerging market economies in the South America (Argentine, Bolivia, Brazil, Columbia) and Asia (India, Indonesia, Malaysia, Philippines, Taiwan, Thailand). We confirm previous results that both distance and border explain a significant amount of relative price variation across different locations. We also find that currency attacks had major disintegration effects by significantly increasing these border effects, and by raising within country relative price dispersion in emerging market economies. These effects are found to be quite persistent since relative price volatility across emerging markets today is still significantly larger than a decade ago. JEL classification: F40, F4

Economic integration and the exchange rate regime: how damaging are currency crises? : [This Version: October 2003]

We use consumer price data for 205 cities/regions in 21 countries to study PPP deviations before, during and after the major currency crises of the 1990s. We combine data from industrialized nations in North America (Unites States, Canada and Mexico), Europe (Germany, Italy, Spain and Portugal), Asia (Japan and South Korea), and Oceania (Australia and New Zealand) with corresponding data from emerging market economies in South America (Argentina, Bolivia, Brazil, Columbia) and Asia (India, Indonesia, Malaysia, Philippines, Taiwan, Thailand). By doing so, we confirm previous results that both distance and border explain a significant amount of relative price variation across different locations. We also find that currency attacks had major disintegration effects by considerably increasing these border effects and by raising within-country relative price dispersion in emerging market economies. These effects are found to be quite persistent since relative price volatility across emerging markets today is still significantly larger than a decade ago

Price stability, inflation convergence and diversity in EMU : does one size fit all?

Using a unique data set of regional inflation rates we are examining the extent and dynamics of inflation dispersion in major EMU countries before and after the introduction of the euro. For both periods, we find strong evidence in favor of mean reversion (ß-convergence) in inflation rates. However, half-lives to convergence are considerable and seem to have increased after 1999. The results indicate that the convergence process is nonlinear in the sense that its speed becomes smaller the further convergence has proceeded. An examination of the dynamics of overall inflation dispersion (ó-convergence) shows that there has been a decline in dispersion in the first half of the 1990s. For the second half of the 1990s, no further decline can be observed. At the end of the sample period, dispersion has even increased. The existence of large persistence in European inflation rates is confirmed when distribution dynamics methodology is applied. At the end of the paper we present evidence for the sustainability of the ECB's inflation target of an EMU-wide average inflation rate of less than but close to 2%. Klassifikation: E31, E52, E5

Inflation rate dispersion and convergence in monetary and economic unions: lessons for the ECB : [This Version November 2005]

Using a set of regional inflation rates we examine the dynamics of inflation dispersion within the U.S.A., Japan and across U.S. and Canadian regions. We find that inflation rate dispersion is significant throughout the sample period in all three samples. Based on methods applied in the empirical growth literature, we provide evidence in favor of significant mean reversion (ß-convergence) in inflation rates in all considered samples. The evidence on ó-convergence is mixed, however. Observed declines in dispersion are usually associated with decreasing overall inflation levels which indicates a positive relationship between mean inflation and overall inflation rate dispersion. Our findings for the within-distribution dynamics of regional inflation rates show that dynamics are largest for Japanese prefectures, followed by U.S. metropolitan areas. For the combined U.S.-Canadian sample, we find a pattern of within-distribution dynamics that is comparable to that found for regions within the European Monetary Union (EMU). In line with findings in the so-called 'border literature' these results suggest that frictions across European markets are at least as large as they are, e.g., across North American markets. Klassifikation: E31, E52, E5